Simultaneous equations · Year 10

In Year 10 you learn: solving by substitution.

Simultaneous equations are two equations with two unknowns that are both true at the same time. Solving them finds the one pair of values that fits both — on a graph, it is the point where the two lines cross.

Key facts

• Elimination: make the coefficients of one letter match, then add the equations (if the signs differ) or subtract them (if the signs are the same).
• Substitution: rearrange one equation for one letter and substitute it into the other.
• Once you have one unknown, substitute back to find the other, then check in both equations.
• Graphically, the solution is where the two graphs intersect.
• With one linear and one quadratic equation, substitute the linear one into the quadratic; there can be 0, 1 or 2 solutions.

Worked examples

Other years

• Simultaneous equations · Year 9
• Simultaneous equations · Year 11
• Simultaneous equations · Year 12